Effective-focal-length calculations and measurements for a radial diffraction grating

As the technology for manufacturing radial diffraction gratings improves, there will be increasing interest in using high-groove-density radial gratings as scales for precision interferometer-type rotary encoders. If efficiency in optical designs is to be optimized, the focusing properties of these gratings must be understood. We use analytical geometry to investigate the focusing properties of a radial diffraction grating illuminated by laser light diverging from a pointlike source. We compare the results with experiments that we performed with a state-of-the-art custom radial grating, and we obtain excellent agreement with our calculations, which improve on earlier analytical work. copyright 1999 Optical Society of America